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The first thing we will look at is the probability in the first dealings, and what kind of predictions we can get out of that. This calculation takes the player into account and does not count on card counting or other cheating practices. These are calculated using one or two decks, not the seven decks used in casinos. First case we want to know is what are the chances we will get a nice initial hand. First things first, the number of combinations that can be made using two cards and one deck is C(52 above 2) = 1326, and if we are to use two decks then C(104 above 2) = 5356. Meaning there are 1326 possible two-card combinations to be made using only 52 cards.
Let us take a look at getting a blackjack :
P = 32/663 = 4,8265% using one deck and P = 64/1339 = 4,7797% using two decks.
That looks highly unlikely so let’s look at these probabilities:
P = 68/663 = 10.2564% using one deck and P = 140/1339 = 10.4556% using two decks for obtaining twenty points first hand.
P = 40/663 = 6.0332% using one deck and P = 80/1339 = 5.9746% using two decks for obtaining  nineteen points the first hand.
P = 43/633 = 6.4857% using one deck and P = 87/1339 = 6.4973% using two decks for obtaining eighteen points the first hand.
P = 16/221 = 7.2398% using one deck and P = 96/1339 = 7.1695% using two decks for obtaining seventeen points the first hand.
Well just let that sink into your brain at it’s own pace. Now straight on to calculating the chance we are getting a nice hand the initial hand. In this case a blackjack,twenty, nineteen or eighteen points and that can be done by adding up all the chances of above. P = 32/663 + 68/663 + 40/663 + 43/663 +43/663 = 183/663 = 27.6018% using just one deck. Not bad and with two decks it is P = 64/1339 + 140/1339 + 80/1339 + 87/1339 = 371/1339 = 27.7072%.
The events during the game are under different rules, it has to be based upon favorable cards. For you as well as the ones the dealer must have, not to mention the other players. Blackjack is all about the strategy based upon the chance you will get the card you want. So on your part you should memorize, or be a very good calculator, to know what you should do.

The calculation used to get a chance value for a certain favorable value x also depends on the number of decks used. As well the number of times it occurs on the table, named nx, and the number of total cards showing, nv. Then the probability of getting the required card the time you ask for it:
P = ( 4 - nx) / ( 52 - nv), if x ≠ 10 and P = (16 - nx) / (52 - nv), if x = 10.
Of course this is only when using one deck if you are using two decks then:
P = ( 8 - nx) / (104 - nv), if x ≠ 10 and P = (32 - nx) / (104 - nv), if x = 10.
In general the formula is when playing with m decks the value x is to be calculated thusly:
P = ( 4*m - nx) / ( 52*m - nv), if x ≠ 10 and P = (16*m - nx) / (52*m - nv), if x = 10.
Now we will set the formula to work, after all the work we did it is time to return the favor. So we are going to play with only one deck, and we are the only player at the table. The cards that lie in front of us are Queen, two, four, Ace (Which add up to 17 points for you sluggish mathematicians) and the other card showing is a four. We are going to use the formula to calculate our chance of getting that four we need.

Before we fill in the numbers, nx = 2 and nv = 5, which results in:
P = ( 4 - 2) / ( 52 - 5) because x ≠ 10; P = 2/47 = 4,2553%

Maybe we should also look into trying to get a three:
P = ( 4 - 0) / ( 52 - 5) ; P = 4/47 = 8,5106%
That looks better maybe the chance to get a two should also be looked at:
P = ( 4 - 1) / ( 52 - 5) ; P = 3/47 = 6,3830%
So now we can calculate the probability to get a two,a three or a four and get a hand that will beat the dealer’s hand. All we do is add up all the chances we calculated. P = 2/47 + 4/47 + 3/47 = 9/47 = 19,1489%. So we have a roughly one in five chance to get a card that will not make us go bust. The chance increases slightly if you also add up the Aces (they can count for one remember).
P = ( 4 - 1) / ( 52 - 5) ; P = 3/47 = 6,3830%. The same as for the two. So the total will add up to P = 12/47 = 25,5319 % . Which is almost exactly one in four. So hitting when you have gotten seventeen like this is not a good gamble but not a long shot. The problem with blackjack is that the players are a variable, the cards are a variable so the situations are astounding in number. Try to memorize a few that are frequent. Or have a really good brain trained at calculating odds at the speed of light. Just for fun let us put this formula to the test with seven decks;

P = ( (4*7) - 2) / ( (52*7) - 5) = 26/359 = 7,2423%. And if we do all the rest of the formulas and add them up we get the total chance of not going bust using seven decks. P = 30,0836%  is a very nice chance like three in ten hands. So you see the more decks you use the more chance you have of a good hand.